Finite Group Databasebeta

← #30605466

Subgroups — #30605466

Order 15616.

580 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461682C211yesmaximal, characteristic
2#21461060C211yesmaximal, characteristic
3#21460814C212yesmaximal, complemented
4#21460813C212yesmaximal, complemented
5#21449179C211yesmaximal, characteristic
6#16840778—21no—
7C2×#14519836—21no—
8#16840704—21no—
9#16840640C2212yes—
10#16840606—21no—
11#16840606C2212yes—
12C22×Q8×D61C411yescharacteristic, complemented
13C2×#14519755—21no—
14C2×#14519739C2211yescharacteristic
15#16839682C411yescharacteristic, complemented
16#16839675C2211yescharacteristic
17#16839673C2211yescharacteristic
18#16839666—21no—
19#16839640—21no—
20#16839633—21no—
21#16839621C411yescharacteristic, complemented
22C61×#395C411yescharacteristic, complemented
23C2×C4⋊#6923—41no—
24C2×C22⋊#6923—22no—
25C4⋊#92420—41no—
26#14519836—42no—
27C22⋊#92420—22no—
28C4×#92420—41no—
29(C2×#6923)⋊C4—41no—
30C22×Dic122—21no—
31C22×Dic122C2×C411yescharacteristic
32C2×Q8×D61—44no—
33C2×Q8×D61—41no—
34C2×Q8×D61—41no—
35C22×D244D411yescharacteristic
36C22×C4×D61—21no—
37C22×C4×D61C2×C411yescharacteristic
38C22×C4×D61D411yescharacteristic
39#14519755—44no—
40#14519739—41no—
41#14519739—41no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198D411yescharacteristic
48C2×#11758198C2311yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684C2×C411yescharacteristic
54C22×Q8×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57#95×C61—21no—
58#95×C61C2×C411yescharacteristic
59C23×D61C22⋊C411yescharacteristic
60C23×D61C2×D411yescharacteristic
61C22×#6923—42no—
62C2×Q8×C61—42no—
63C2×Q8×C61—41no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73Q8×D61—44no—
74Q8×D61—44no—
75Q8×D61—44no—
76Q8×D61—44no—
77C2×D244—41no—
78C2×D244—41no—
79C2×D244SD1612yes—
80C2×D244Q1612yes—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—42no—
86C2×C4×D61—42no—
87C2×C4×D61—42no—
88C2×C4×D61—42no—
89C2×C4×D61—42no—
90C2×Dic122—24no—
91C2×Dic122—42no—
92C2×Dic122—41no—
93C2×Dic122—41no—
94C2×Dic122—41no—
95C2×Dic122—42no—
96C22⋊#6923—42no—
97C22⋊#6923—42no—
98C2×#92420—42no—
99C4⋊#6923—82no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—42no—
102#11758198—41no—
103#11758198—41no—
104#11758198—42no—
105#11758198—42no—
106#11758198—42no—
107#11758196—42no—
108#11758196—42no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C23×C61C2×C22⋊C411yescharacteristic
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61#10312yes—
121C22×D61C2×SD1611yescharacteristic
122C22×D61C2×Q1611yescharacteristic
123C2×#6923—82no—
124C2×#6923—82no—
125C2×#6923—82no—
126Q8×C61—42no—
127Q8×C61—42no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—22no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61#10312yes—
141C2×Dic61—22no—
142C2×Dic61—22no—
143C2×Dic61—21no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61#9911yescharacteristic
151C2×Dic61#9911yescharacteristic
152D244—42no—
153D244—42no—
154C4×D61—42no—
155C4×D61—48no—
156C4×D61—42no—
157C4×D61—42no—
158C4×D61—81no—
159Dic122—44no—
160Dic122—42no—
161Dic122—44no—
162Dic122—42no—
163#92420—82no—
164#11898—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61C2×#9911yescharacteristic
168C22×C61C2×#10311yescharacteristic
169C22×C61#42111yescharacteristic
170C2×D61—21no—
171C2×D61—22no—
172C2×D61—21no—
173C2×D61—42no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—42no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—81no—
182#6923—162no—
183C4×C61—22no—
184C4×C61—42no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61—81no—
188Dic61—21no—
189Dic61—42no—
190Dic61—41no—
191Dic61—81no—
192Dic61AΣL(1,𝔽16)12yes—
193#2409—611no—
194#1799—611no—
195#1460—611no—
196#1351—612no—
197#1351—612no—
198C2×C61—21no—
199C2×C61—21no—
200C2×C61#152011yescharacteristic
201C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
202C2×C61#212911yescharacteristic
203D61—41no—
204D61—42no—
205D61—41no—
206C23×Q8—611no—
207C2×C22⋊Q8—1221no—
208C2×C4×D4—611no—
209#431—1221no—
210C2×#99—1221no—
211#395—611no—
212#395#692311yescharacteristic, complemented
213#393—611no—
214#393—611no—
215#391—1221no—
216#386—1221no—
217#385—1221no—
218#380—611no—
219#380—1221no—
220#342—612no—
221#323—612no—
222#323—1221no—
223C61#1189811yescharacteristic, complemented, Sylow
224C22×Q8—611no—
225C22×Q8—1221no—
226C22×Q8—2441no—
227C22×Q8—2441no—
228C22×Q8—2444no—
229C22×Q8C2×#692311yescharacteristic
230C22×D4—611no—
231C23×C4—611no—
232C23×C4—611no—
233C23×C4—1221no—
234C22⋊Q8—2444no—
235C4×D4—2441no—
236C4×D4—2441no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4—2441no—
241C2×C4⋊C4C2×#692311yescharacteristic
242C2×C22⋊C4—611no—
243C2×C22⋊C4—611no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C22⋊C4—1222no—
248C2×C42—611no—
249C4⋊C8—2441no—
250#99—2442no—
251C22⋊C8—1222no—
252C4×C8—2441no—
253#95—21no—
254#95—611no—
255#95—1221no—
256#95—1221no—
257#95—1221no—
258#95—2441no—
259#95C2×#692311yescharacteristic
260C24—611no—
261C24—611no—
262C2×Q8—42no—
263C2×Q8—41no—
264C2×Q8—1224no—
265C2×Q8—2441no—
266C2×Q8—2441no—
267C2×Q8—2441no—
268C2×Q8—2442no—
269C2×Q8—2442no—
270C2×Q8—2444no—
271C2×Q8—2444no—
272C2×Q8—2444no—
273C2×Q8—2444no—
274C2×D4—612no—
275C2×D4—612no—
276C2×D4—2441no—
277C2×D4—2441no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—2442no—
289C22×C4—2442no—
290C22×C4—2442no—
291C22×C4—2442no—
292C22×C4—2442no—
293C22×C4—2442no—
294C22×C4C22⋊#692311yescharacteristic
295C22×C4C22⋊#692311yescharacteristic
296C22×C4C22×#692311yescharacteristic
297C2×C8—2442no—
298C4⋊C4—41no—
299C4⋊C4—42no—
300C4⋊C4—4882no—
301C4⋊C4—2442no—
302C4⋊C4—2442no—
303C22⋊C4—2441no—
304C22⋊C4—2441no—
305C22⋊C4—2442no—
306C22⋊C4—2442no—
307C22⋊C4—2442no—
308C22⋊C4—2442no—
309C22⋊C4—2442no—
310C42—1221no—
311C42—1221no—
312C23—612no—
313C23—611no—
314C23—611no—
315C23—1221no—
316C23—1221no—
317C23—1221no—
318C23—1221no—
319C23—2441no—
320C23—2441no—
321C23—2441no—
322C23—2441no—
323C23C2×C22⋊#692311yescharacteristic
324Q8—42no—
325Q8—42no—
326Q8—2444no—
327Q8—2444no—
328Q8—2442no—
329Q8—2442no—
330D4—2442no—
331D4—2442no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—1222no—
347C2×C4—1222no—
348C2×C4—1221no—
349C2×C4—4881no—
350C2×C4—4882no—
351C2×C4—4882no—
352C2×C4—4882no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4—2442no—
356C2×C4—2448no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4#1451984012yes—
364C8—4882no—
365C22—21no—
366C22—21no—
367C22—1221no—
368C22—1221no—
369C22—1222no—
370C22—4881no—
371C22—2441no—
372C22—2441no—
373C22—2442no—
374C22—2442no—
375C22—2441no—
376C22—2441no—
377C22—2441no—
378C22—2441no—
379C22D61⋊#9911yescharacteristic
380C22C2×#1451984011yescharacteristic
381C22#1684075911yescharacteristic
382C4—22no—
383C4—42no—
384C4—41no—
385C4—41no—
386C4—81no—
387C4—612no—
388C4—1221no—
389C4—9762no—
390C4—4881no—
391C4—2442no—
392C4—2441no—
393C2—21no—
394C2—21no—
395C2—2441no—
396C2—2441no—
397C2—2442no—
398C2#2146125711yescharacteristic
399C2D61⋊AΣL(1,𝔽16)11yescharacteristic
400C2#2146210211yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#395C4
socleC22×C61C2×#99
prime radicalC22×D244D4
cosocleC2×#11758198C23
hypercenter#395#6923
hypocenterC61#11898
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #395

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #21460814C2semidirect
4. #21460813C2semidirect
12. C22×Q8×D61C4semidirect
15. #16839682C4semidirect
21. #16839621C4semidirect
22. C61×#395C4semidirect
212. #395#6923semidirect
223. C61#11898semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214616822
#214610602
#214608142
#214608132
#214491792
#1189861